Ramanujan’s Contributions to Eisenstein Series, Especially in His Lost Notebook
نویسنده
چکیده
where Bn, n ≥ 0, denotes the nth Bernoulli number, and where σν(n) = ∑ d|n d ν . The latter two representations in (1.1) can be established by using the Lipschitz summation formula or Fourier analysis. For these and other basic properties of Eisenstein series, see, for example, R. A. Rankin’s text [41, Chap. 6]. In Ramanujan’s notation, the three most relevant Eisenstein series are defined for |q| < 1 by
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